The Strong Law of Large Numbers and the Entropy Ergodic Theorem for Nonhomogeneous Bifurcating Markov Chains Indexed by a Binary Tree
Guyon (Guyon J. Limit theorems for bifurcating Markov chains. Application to the detection of cellular aging. Ann Appl Probab, 2007, 17: 1538-1569) introduced an important model for homogeneous bifurcating Markov chains indexed by a binary tree taking values in general state space and studied their...
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| creator | Dang, Hui Yang, Weiguo Shi, Zhiyan |
| description | Guyon (Guyon J. Limit theorems for bifurcating Markov chains. Application to the detection of cellular aging. Ann Appl Probab, 2007, 17: 1538-1569) introduced an important model for homogeneous bifurcating Markov chains indexed by a binary tree taking values in general state space and studied their limit theorems. The results were applied to detect cellular aging. In this paper, we define a discrete form of nonhomogeneous bifurcating Markov chains indexed by a binary tree and discuss the equivalent properties for them. The strong law of large numbers and the entropy ergodic theorem are studied for these Markov chains with finite state space. In contrast to previous work, we use a new approach to prove the main results of this paper. |
| doi_str_mv | 10.1109/TIT.2015.2404310 |
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Limit theorems for bifurcating Markov chains. Application to the detection of cellular aging. Ann Appl Probab, 2007, 17: 1538-1569) introduced an important model for homogeneous bifurcating Markov chains indexed by a binary tree taking values in general state space and studied their limit theorems. The results were applied to detect cellular aging. In this paper, we define a discrete form of nonhomogeneous bifurcating Markov chains indexed by a binary tree and discuss the equivalent properties for them. The strong law of large numbers and the entropy ergodic theorem are studied for these Markov chains with finite state space. 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Limit theorems for bifurcating Markov chains. Application to the detection of cellular aging. Ann Appl Probab, 2007, 17: 1538-1569) introduced an important model for homogeneous bifurcating Markov chains indexed by a binary tree taking values in general state space and studied their limit theorems. The results were applied to detect cellular aging. In this paper, we define a discrete form of nonhomogeneous bifurcating Markov chains indexed by a binary tree and discuss the equivalent properties for them. The strong law of large numbers and the entropy ergodic theorem are studied for these Markov chains with finite state space. In contrast to previous work, we use a new approach to prove the main results of this paper.</description><subject>Aging</subject><subject>binary tree</subject><subject>Binary trees</subject><subject>Convergence</subject><subject>Educational institutions</subject><subject>Entropy</subject><subject>entropy ergodic theorem</subject><subject>Markov analysis</subject><subject>Markov processes</subject><subject>nonhomogeneous bifurcating Markov chains</subject><subject>Numbers</subject><subject>Random variables</subject><subject>strong law of large numbers</subject><subject>Theorems</subject><issn>0018-9448</issn><issn>1557-9654</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2015</creationdate><recordtype>article</recordtype><sourceid>RIE</sourceid><recordid>eNo9kMFOwzAQRC0EEqVwR-JiiXPKOnHs5AhVgUqlHAjnyEnWbQqxi50A_QD-G1dFnEYrvZndHUIuGUwYg_ymmBeTGFg6iTnwhMERGbE0lVEuUn5MRgAsi3LOs1Ny5v0mjDxl8Yj8FGukL72zZkUX6otaHcStkC6HrkLnqTIN7QMzMwHa7ujMrWzT1jT4rMOOauvo0pq17ewKDdrB07tWD65WfRsyn5R7s590ulat8XRuGvzGhlY7qgJmlNvRwiGekxOt3j1e_OmYvN7PiuljtHh-mE9vF1Ed56yPdK0anSOXilcVB8iYSgXINE54JXkTK5bkMnydYK4rIUBhg1le6QRAZBJlMibXh9ytsx8D-r7c2MGZsLJkQogskcAhUHCgame9d6jLrWu7cGvJoNyXXYayy33Z5V_ZwXJ1sLSI-I-HtFgKkfwCro57Dw</recordid><startdate>201504</startdate><enddate>201504</enddate><creator>Dang, Hui</creator><creator>Yang, Weiguo</creator><creator>Shi, Zhiyan</creator><general>IEEE</general><general>The Institute of Electrical and Electronics Engineers, Inc. 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Limit theorems for bifurcating Markov chains. Application to the detection of cellular aging. Ann Appl Probab, 2007, 17: 1538-1569) introduced an important model for homogeneous bifurcating Markov chains indexed by a binary tree taking values in general state space and studied their limit theorems. The results were applied to detect cellular aging. In this paper, we define a discrete form of nonhomogeneous bifurcating Markov chains indexed by a binary tree and discuss the equivalent properties for them. The strong law of large numbers and the entropy ergodic theorem are studied for these Markov chains with finite state space. In contrast to previous work, we use a new approach to prove the main results of this paper.</abstract><cop>New York</cop><pub>IEEE</pub><doi>10.1109/TIT.2015.2404310</doi><tpages>9</tpages></addata></record> |
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| subjects | Aging binary tree Binary trees Convergence Educational institutions Entropy entropy ergodic theorem Markov analysis Markov processes nonhomogeneous bifurcating Markov chains Numbers Random variables strong law of large numbers Theorems |
| title | The Strong Law of Large Numbers and the Entropy Ergodic Theorem for Nonhomogeneous Bifurcating Markov Chains Indexed by a Binary Tree |
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